Problem: Simplify; express your answer in exponential form. Assume $x\neq 0, t\neq 0$. $\dfrac{{(x)^{5}}}{{(x^{-2}t^{-2})^{-5}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x}$ to the exponent ${5}$ . Now ${1 \times 5 = 5}$ , so ${(x)^{5} = x^{5}}$ In the denominator, we can use the distributive property of exponents. ${(x^{-2}t^{-2})^{-5} = (x^{-2})^{-5}(t^{-2})^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(x)^{5}}}{{(x^{-2}t^{-2})^{-5}}} = \dfrac{{x^{5}}}{{x^{10}t^{10}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{5}}}{{x^{10}t^{10}}} = \dfrac{{x^{5}}}{{x^{10}}} \cdot \dfrac{{1}}{{t^{10}}} = x^{{5} - {10}} \cdot t^{- {10}} = x^{-5}t^{-10}$.